Related papers: On intervals in some posets of forests
Starting from the data of an arbor, which is a rooted tree with vertices decorated by disjoint sets, we introduce a lattice polytope and a partial order on its lattice points. We give recursive algorithms for various classical invariants of…
This study is dedicated to precise distributional analyses of the height of non-plane unlabelled binary trees ("Otter trees"), when trees of a given size are taken with equal likelihood. The height of a rooted tree of size $n$ is proved to…
We find surprisingly simple formulas for the limiting probability that the rank of a randomly selected vertex in a randomly selected phylogenetic tree or generalized phylogenetic tree is a given integer.
We initiate the combinatorial study of factorization systems on finite lattices, paying special attention to the role that reflective and coreflective factorization systems play in partitioning the poset of factorization systems on a fixed…
For a pair consisting of a gene tree and a species tree, the ancestral configurations at an internal node of the species tree are the distinct sets of gene lineages that can be present at that node. Ancestral configurations appear in…
In this article, some factorization properties of polynomials over discrete valuation domains are elucidated. These properties along with the notion of Newton index of a polynomial leads to a generalization of the main result proved by…
We give correct explicit formulas for the probabilities of rooted binary trees and cladograms under Ford's $\alpha$-model.
We propose a modification that corrects for split-improvement variable importance measures in Random Forests and other tree-based methods. These methods have been shown to be biased towards increasing the importance of features with more…
The hierarchical and recursive expressive capability of rooted trees is applicable to represent statistical models in various areas, such as data compression, image processing, and machine learning. On the other hand, such hierarchical…
We introduce new combinatorial objects, the interval- posets, that encode intervals of the Tamari lattice. We then find a combinatorial interpretation of the bilinear operator that appears in the functional equation of Tamari intervals…
We introduce a notion of finite sampling consistency for phylogenetic trees and show that the set of finitely sampling consistent and exchangeable distributions on n leaf phylogenetic trees is a polytope. We use this polytope to show that…
In weighted trees, all edges are endowed with positive integral weight. We enumerate weighted bicolored plane trees according to their weight and number of edges.
We assess advantages of expressing tree-structured Ising models via their mean parameterization rather than their commonly chosen canonical parameterization. This includes fixedness of marginal distributions, often convenient for dependence…
We introduce a new matroid (graph) invariant, the arboricity polynomial. Given a matroid, the arboricity polynomial enumerates the number of covers of the ground set by disjoint independent sets. We establish the polynomiality of the…
Regular tree grammars and regular path expressions constitute core constructs widely used in programming languages and type systems. Nevertheless, there has been little research so far on reasoning frameworks for path expressions where node…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
We prove a fix point theorem for monoids of self-embeddings of trees. As a corollary, we obtain a result by Laflamme, Pouzet and Sauer that a tree either contains a subdivided binary tree as a subtree or has a vertex, and edge, an end or…
The aim of this note is to describe the structure of finite meadows. We will show that the class of finite meadows is the closure of the class of finite fields under finite products. As a corollary, we obtain a unique representation of…
We analyze the interplay between labeled trees and the ultrametric spaces they present. We provide characterizations of labeled trees that generate separable ultrametric spaces and those that generate locally finite ultrametric spaces. In…
We propose Partition Tree, a novel tree-based framework for conditional density estimation over general outcome spaces that supports both continuous and categorical variables within a unified formulation. Our approach models conditional…